Is there any artificially intelligent system that really mimics human intelligence?
As far as emulating an intelligent being, no. There are a few different potential architectures for possible AGI. Many of these are extremely infantile, as the bulk of AI research is in narrow AI, which focuses on creating algorithms that are highly specialized for a specific task.

With that being said, here is one supervised learning approach to this problem by Andrej Karpathy: Karpathy Method

OpenAI, also has a team who works on the AGI problem.